Cognitive representations of peer relationships were conceptualised as the attributions children make about the intentions of others and children's peer affiliation, or desire to interact with peers. Measures of these two constructs were developed and administered to 55 four- to six-year-olds. Findings indicate that measures of both measures of cognitive representations were associated with teacher-rated peer competence, even when standardised Peabody Picture Vocabulary Test scores were controlled. The association between peer affiliation and peer competence was mediated by strategy response generation, while the association between attributions and peer competence was direct. Father-child synchrony during a laboratory play session was associated with peer competence, and this association appeared to be at least partially mediated by response generation and peer affiliation scores. (Contains 2 tables and 1 figure.)